Minimizers of the Lawrence-Doniach model under weak coupling and a parallel or slightly tilted field

Zhenqiu Xie, Purdue University

Abstract

We consider minimizers to the Lawrence-Doniach energy for superconductors with coupled layer structures. When the exterior magnetic field is parallel or slightly tilted to the layers and the Josephson coupling between layers is weak enough, we prove that the global minimizer has no vortices on layers. From this we derive upper and lower bounds on the upper and lower critical fields of the superconductor along different directions, when the coupling is weak. Besides the N-dimensional torus formed by minimizers in the decoupled case, we consider weak coupling cases and use Lyapunov-Schmidt techniques to identify the equilibria of the energy functional with low energies as a finite number of curves of solutions connected to the torus, expressed as C1 functions of the coupling constant, with one curve being the unique global minimizers. We also prove stability and obtain detailed information on the nature of the order parameter on each layer and the induced magnetic field in this case. Our results show that in this setting, even in large magnetic fields, stable solutions without vortices can occur with the order parameters having a nearly uniform phase jump between adjacent layers.

Degree

Ph.D.

Advisors

Bauman, Purdue University.

Subject Area

Applied Mathematics|High Temperature Physics

COinS